this question is hard to answer as there can be so many different scenarios.

If you start NUTANIX Snapshots which trigger VMware Tools quiescense (which trigger minimal VSS processing for consistency) another backup tool should not start a VSS processing at same time.
Depending on the running application, this is in most cases no real issue, as the VSS proccessing take only some seconds and the consistency stage is released after some seconds when Nutanix or Veeam has created a snapshot.

What could happen is that Nutanix or Veeam fail if you start this at same time. If you want to do this more coordinated, maybe a post Veeam script could start the Nutanix snapshot?